Unformatted text preview: s of y = f (x) and y = g (x), where both the solution to x and y are of interest, we have
what is known as a system of equations, usually written as
y = f (x)
y = g (x)
The ‘curly bracket’ notation means we are to ﬁnd all pairs of points (x, y ) which satisfy both
equations. We begin our study of systems of equations by reviewing some basic notions from
Definition 8.1. A linear equation in two variables is an equation of the form a1 x + a2 y = c
where a1 , a2 and c are real numbers and at least one of a1 and a2 is nonzero.
For reasons which will become clear later in the section, we are using subscripts in Deﬁnition 8.1
to indicate diﬀerent, but ﬁxed, real numbers and those subscripts have no mathematical meaning
beyond that. For example, 3x − y = 0.1 is a linear equation in two variables with a1 = 3, a2 = − 1
and c = 0.1. We can also consider x = 5 to be a linear equation in two variables by identifying
a1 = 1, a2 = 0, and c = 5.1 If a1 and a2 are both 0, then depending on c, we get eit...
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